Lecture Notes on Unit Conversions, Dimensional Analysis, and Density

Flashcards about unit conversions, dimensional analysis, and density; key concepts and definitions from the lecture notes.

How should you set up unit conversions?

Always set up the problem so that the units you don't want cancel out, leaving you with the units you do want.

If you get an answer that doesn't seem right when doing unit conversions, what should you do?

Check if you used the right conversion factor, if it was flipped, and if your math is correct.

What's the easiest way to write out a fractional unit?

Use a fraction, with the volume unit always getting a '1'.

How do significant figures work in conversion factors?

They are usually exact numbers and do not determine significant figures; sig figs are determined by the starting number.

List metric conversions you need to memorize.

One meter is equal to 100 centimeters. One meter is equal to 1000 millimeters. 1000 meters is equal to one kilometer. One gram is equal to 100 centigrams. One gram is equal to 1000 milligrams. 1000 grams is one kilogram. 1000 liters equals one kiloliter. One second is 100 milliseconds. One second is 1000 milliseconds. One cubic centimeter is the same as one milliliter.

When doing multiple conversions, is it better to do each conversion separately or all together?

It's usually best to write out the full conversion, allowing the calculator to carry the answer down, to avoid retyping errors.

How can fractional units be used in conversions?

A fractional unit can provide a conversion between distance and time (e.g., miles per hour).

How do you convert from degrees Celsius to Kelvin?

Add 273.15 to the Celsius temperature. When converting between degrees Celsius and Kelvin, this is the only conversion that will follow addition/subtraction sig fig rules.

How do you convert from Kelvin to degrees Celsius?

Subtract 273.15 from the temperature in Kelvin.

Define length, mass, and volume and give their SI units.

Length is the measurement between two points and its SI unit is meters. Mass is the amount of matter and its SI unit is kilograms. Volume is how much space something takes up, and its SI unit is cubic meters.

What does temperature measure?

Kinetic energy at the molecular level.

What is the equation for density?

Mass over volume (m/v)

What are some common units for density?

Grams per milliliter (g/mL) is typical for fluids; Kilograms per meter cubed (kg/m^3) is used in engineering.

What are things that can be considered a fluid?

Liquids and gasses

How does temperature affect density?

As temperature increases, volume typically increases, and density decreases.

What is the density of water (without being given a specific temperature)?

At 4 degrees Celsius, the density of water is approximately 1.00 g/mL.

Does mass or volume change with temperature?

The mass does not change, but the volume does change depending on the temperature.

When a substance gets colder, what happens?

Water expands, whereas other substances contract.

In a mixture, how do densities behave in relation to height

Lower densities rise to the top, while higher densities sink to the bottom.

What is Archimedes' principle?

Archimedes' principle involves measuring the apparent loss of weight of an object submerged in a fluid to determine its volume.

List formulas to calculate volume.

Volume = length x width x height, Volume = Area times thickness, Volume of a cylinder is pir^2height, volume of a sphere 4/3pir^3.

Water Displacement

A quick, dirty way of measuring volume.

How is density related to mass and volume?

Density is the critical conversion between mass and volume. Density is mass over volume and is measured in grams per cubic centimeter.

How can you find the mass of water displaced knowing the buoyant force?

The mass of water displaced = (density of water) * (volume of object).

What is specific gravity?

A ratio of the density of a substance to the density of water; it is unitless.

What instrument is used to measure specific gravity?

A hydrometer. You measure where the bottom of the meniscus meets with the tool to get the specific gravity.